Prime divisors and birational geometry in Fano manifolds
Lundi, 3 Février, 2014 - 10:30
Résumé :
Let X be a smooth, complex Fano variety, D a prime divisor in X, and set c(D):=dim ker(r:H2(X,R)->H2(D,R)), where r is the natural restriction map. It is a special property of Fano manifolds that the presence of a prime divisor D with large c(D) has consequences on the geometry of X. More precisely, we define c_X:=max{c(D)|D is a prime divisor in X}. Then c_X\leq 8, and if c_X is at least 2, then we get some special properties of X. We will explain this result, which relies on a construction in birational geometry; then we will focus on the case c_X=2.
Institution de l'orateur :
U. Torino
Thème de recherche :
Algèbre et géométries
Salle :
4